We propose to apply the group fused Lasso to estimate time series models with endogenous regressors and an unknown number of breaks. It can correctly determine the number of breaks and estimate the break dates asymptotically. Simulations and applications are given.

We give two new approaches to testing conditional exogeneity. This condition ensures unconfoundedness and identification of structural effects. Our approaches permit the presence of treatment effects under the null, thereby complementing methods of Rosenbaum (1987) and Heckman and Hotz (1989).